This invention relates to a calculator for calculating an exponential function a.sup.x with the base a of an optional positive number. The exponent or power x is a real number throughout the specification, unless otherwise specified. It should also be noted that the "function" as called herein means a specific value of the function for a certain given value of the independent variable.
It is often required in scientific calculation to calculate with a calculator an exponential function e.sup.x or expx with the base e, known as the base of natural logarithm, and another exponential function 10.sup.x with the base ten. Most of the calculators for scientific use therefore have subroutines stored therein for calculation of such special exponential functions. On the other hand, it is not seldom to feel the necessity of calculating a general exponential function a.sup.x with the base a, where the base a is a positive number other than e and ten. On calculating the general exponential function a.sup.x with a conventional scientific calculator, it is necessary to calculate at first lna, where the operator "ln" represent natural logarithm, and then x(lna). By the use of the calculated value of x(lna), it is now possible to calculate the value of exp[x(lna)], namely, the general exponential function a.sup.x.
A conventional scientific calculator is thus inconvenient. Moreover, the calculator has to comprise a complicated circuit for carrying out preliminary calculations even for calculation of the specific exponential function e.sup.x. The subroutine for calculating the desired value of e.sup.x is to resort to the power series for e.sup.x known as: EQU e.sup.x =1+x/1!+x.sup.2 /2!+x.sup.3 /3!+ . . . ,
Which series converges only slowly unless the absolute value of x is smaller than unity. The preliminary calculation circuit is for modifying the given value of x so as to make the power series converge rapidly. At any rate, use of the power series reduces the speed of calculation.